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3 years ago

Explain how you could get a formula for the volume of the glass.

Mathematics

1 answer:

harkovskaia [24]3 years ago

6 0

Answer:

Step-by-step explanation:

a. find the vertical height of the bowl of glass

b.calculate the volume of the bowl of each glass

c.find the height of the water

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I have these factoring questions I need help with.

snow_lady [41]

$f(x)=4x^2+4x-3$

1. Determine y-intercept.

The y-intercept is (0,-3). Substitute x = 0 in the equation as we get f(x) = -3 as the y-intercept.

2. Determine the zeros.

Factor the polynomials first. $(2x-1)(2x+3)$ This is the factored form. The zeros are the roots of equation. Therefore, the zeros are 1/2 and -3/2

3. Determine the Axis of Symmetry

We can solve this by using the formula of $x=-\frac{b}{2a}$ However, I'll be solving the Axis of Symmetry with Calculus instead.

$f'(x)=2(4x^{2-1})+1(4x^{1-1})-0\\f'(x)=8x+4$

Then let f'(x) = 0 to find the Axis of Symmetry.

$8x+4=0\\8x=-4\\x=-\frac{4}{8}\\x=-\frac{1}{2}$

Therefore, the Axis of Symmetry is -1/2

4. Determine the vertex.

Substitute the value of Axis of Symmetry in f(x).

$f(x)=4(-\frac{1}{2})^2+4(-\frac{1}{2})-3\\f(x)=4(\frac{1}{4})-2-3\\f(x)=1-2-3\\f(x)=-4$

Therefore the vertex is at (-1/2, -4)

5. Does the vertex representing max-pont or min-point?

The vertex represents the minimum point. The graph is upward, meaning the minimum point is the point that gives the LOWEST Y-VALUE.

7. Graph f(x)

Unfortunately I won't be able to graph. But I can tell you to graph a parabola that has the most curve at the vertex and intercepts y-axis at (0,-3).

--------------------------- End of Part 1 --------------------------------

2. Write the general form of Quadratic Function in standard form.

$y=ax^2+bx+c$

The graph can be easily determined about the y-intercept and being an upward or downward parabola along with how narrow or wide the parabola is.

For example, c value is the y-intercept as defined. When a > 0, the parabola is upward and when a < 0, the parabola is downward. The more value of | a | is, the more narrow it will be and the less value of | a | it is, the wider it will be.

3. Write in Factored Form

$y=(x+a)(x+b)\\y=(x-a)(x-b)\\y=(x+a)(x-b)\\y=(x-a)(x+b)$

These are factored forms with different types of operators.

The equation can be easily determined about the roots of equation. For example, if the function is in f(x) = (x+2)(x-1) Then the roots would be x = -2 and 1 as the graph will intercept x-axis at (-2,0) and (1,0)

4. Write in Vertex Form.

$y=a(x-h)^2+k$

The equation can be easily determined for the vertex, axis of symmetry and the same narrow/wide/upward/downward parabola again.

The vertex is at (h,k) and the axis of symmetry is at x = h.

For example, $y=(x-2)^2+3$

The vertex would be at (2,3) and the axis of symmetry is x = 2.

3 0

3 years ago

The lowest point in Death Valley is Badwater at 282 feet below sea level. The highest point in

Finger [1]

Answer:

Step-by-step explanation:

Given

$Badwater = -282ft$

$Telescope\ Peak = 11043ft$

The position of badwater is negated because it is below sea level

The interpretation of the question, is to calculate the distance between the two given points.

This is calculated as:

$Difference = Telescope\ Peak - Badwater$

$Difference = 11043ft - (-282ft)$

Open bracket

$Difference = 11043ft+282ft$

$Difference = 11325ft$

Hence, the distance between both is 11325ft

8 0

3 years ago

How do I draw Traingles with ASA similarity??

natulia [17]

Answer:

Step-by-step explanation:

7 0

3 years ago

-18>1.5q solve the inequality. Graph the solution.

inysia [295]

Answer:

q < - 12

Step-by-step explanation:

1.5q < - 18

4 0

3 years ago

Table below shows the age in years and the retail value in thousands of dollars of a random sample of ten automobiles of the sam

horrorfan [7]

Answer:

Step-by-step explanation:

Hello!

Given the study variables

X: Age of an automobile (years)

Y: Retail value of an automobile (thousands of dollars)

a) Construct a scatter diagram.

(attached image)

b) Compute the linear correlation coefficient r. Interpret its value in the context of the problem.

The formula for the correlation coefficient (Person) is:

$r= \frac{sum(XY)-\frac{sum(X)*sum(Y)}{n} }{[sum(X^2)-\frac{(sum(X))^2}{n}] * [sum(Y^2)-\frac{(sum(Y))^2}{n} ] }$

First you have to do some intermediate summatories:

∑x= 40

∑x²= 174

∑y= 246.30

∑y²= 6154.15

∑xy= 956.5

$r= \frac{956.5-\frac{40*246.3}{10} }{[147-\frac{(40)^2}{10}] * [6154.15-\frac{(246.3)^2}{10} ] }$

r= -0.818 ≅ 0.82

-0.82 indicates there is a strong negative linear correlation between the age of the automobiles and the retail price. Wich means that the older the car, the less it costs.

c) Compute the least squares regression line. Plot it on the scatter diagram.

Interpret the meaning of the slope of the least-squares regression line in the context of the problem.

The least squares regression line is Y= a + bX

To calculate the regression line you need to calculate the values of "a" and "b"

$a= (\frac{sum(Y)}{n} ) -b(\frac{sum(X)}{n} )$

$a= (\frac{246.3}{10} ) -(-2.05)(\frac{40}{10} )$

a= 32.83

$b= \frac{sum(XY)-\frac{sum(X)*sum(Y)}{n} }{sum(X^2)-(\frac{sum(X)^2}{n})}$

$b= \frac{956.5-\frac{40*246.3}{10} }{174-(\frac{40^2}{10})}$

b= -2.05

Y= 32.83 - 2.05X

Check attachment for graphic.

-2.05 $(\frac{years}{thousanfs of dollars})$ is the modification of the estimated mean of the retail value of automobiles every time their age increases one year. In other words, every time the automobiles increase their age in one year, the price decreases 2.05 thousands of dollars.

e) Suppose a 20 -year-old automobile of this make and model is selected at random. Use the regression equation to predict its retail value. Interpret the result.

You need to calculate the value of Y for a value of X of 20 years. To do so you replace the values in the regression equation:

Y= 32.83 - 2.05(20)

Y= -8.17 thousands of dollars.

Under the model Y= 32.83 - 2.05X, a 20-year-old automobile has a retail price of -8.17 thousands of dollars.

This is mathematically correct even if it doesn't make sense in context.

f) Comment on the validity of using the regression equation to predict the price of a brand new automobile of this make and model.

You can only use the regression equation to predict possible values of Y for values of X that are between the range of definition of the variable. In this case, the variable is defined in numbers from 2 to 6 years.

You can predict values outside the range of definition of X but the further these values are from the definition range, the less accurate and imprecise the prediction is.

For example in question e) I've predicted the value of Y for X= 20 years, although I've obtained a result truth is that this prediction is not accurate nor reliable.

I hope it helps!

8 0

4 years ago